11.3 Summary

11.3 Summary#

This section summarises the key steps and syntax for specifying, fitting, inspecting, and visualising CFA and SEM models using semopy.

Specifying a Model#

In SEM, models are defined using a string-based syntax that separates the measurement model (relationships between observed and latent variables) from the structural model (relationships between latent variables).

desc = '''# Measurement model
          latent_factor1 =~ x1 + x2 + x3
          latent_factor2 =~ x4 + x5 + x6

          # Structural model
          latent_factor2 ~ latent_factor1'''

This example specifies two latent variables, each measured by three observed variables, and a structural regression in which latent_factor1 predicts latent_factor2.

Higher-order Factors#

Latent variables can themselves be indicators of a higher-order latent variable:

desc = '''# First-order measurement model
          latent_factor1 =~ x1 + x2 + x3
          latent_factor2 =~ x4 + x5 + x6

          # Higher-order factor
          general_factor =~ latent_factor1 + latent_factor2'''

Variances and Covariances#

Variances and covariances are specified using the ~~ operator:

desc = '''latent_factor1 =~ x1 + x2 + x3
          latent_factor2 =~ x4 + x5 + x6

          # Allow latent factors to covary
          latent_factor1 ~~ latent_factor2
          '''

Covariances can be fixed to zero to impose independence assumptions:

latent_factor1 ~~ 0*latent_factor2

Overview of Operators#

  • =~ associates observed variables with latent factors (and latent factors with higher-order factors)

  • ~ specifies regression relationships

  • ~~ specifies variances and covariances

Fitting a Model#

model = semopy.Model(desc)
model_fit = model.fit(data)

Extracting Model Estimates#

estimates = model.inspect(std_est=True)
print(estimates)

Extracting Fit Measures#

stats = semopy.calc_stats(model)
print(stats.T)

Visualising the Model#

semopy.semplot(model, plot_covs=True, std_ests=True, filename='data/plot.pdf')

Key Takeaways

  • CFA focuses on the measurement model; SEM extends CFA by adding directional relationships between latent variables.

  • SEM models consist of a measurement model and a structural model.

  • Individual parameter estimates and overall model fit address different questions and must be interpreted jointly.

  • Standardised estimates aid interpretation, while unstandardised estimates are required for statistical inference.

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